POTW115 Solution

Answer to POTW115 is 12877.

We can decompose
\displaystyle \sum_{k=2}^{101} \frac{1}{(k-1) \times k \times (k+1)} = \sum_{k=2}^{101} \frac{1}{2(k-1)} - \frac{1}{2k} + \frac{1}{2k+1} - \frac{1}{2k}.

The remaining terms are
\displaystyle \frac{1}{2} - \frac{1}{202} + \frac{1}{204} - \frac{1}{4} = \frac{2575}{10302}.

So a+b = 2575 + 10302 = 12877.

By PC Toh, on September 6, 2013 at 5:30 am, under POTW Solutions. No Comments
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